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Data Analysis

Chapter 8

In this chapter, we focus on 3 parts

Chapter 6

Data Analysis

- 1. Descriptive Analysis
- 2. Two-way Analysis of Variance
- 3. Forecasting

1. Descriptive Analysis

Chapter 6

Data Analysis

- 1.1 Index Numbers
- 1.2 Exponential Smoothing

1.1 Index Numbers

Chapter 6

Data Analysis

- Index Number a number that measures the change

in a variable over time relative to the value of

the variable during a specific base period - Simple Index Number index based on the relative

changes (over time) in the price or quantity of a

single commodity

1.1 Index Numbers

Chapter 6

Data Analysis

- Laspeyres and Paasche Indexes compared
- The Laspeyres Index weights by the purchase

quantities of the baseline period - The Paasche Index weights by the purchase

quantities of the period the index value

represents. - Laspeyres Index is most appropriate when baseline

purchase quantities are reasonable approximations

of purchases in subsequent periods. - Paasche Index is most appropriate when you want

to compare current to baseline prices at current

purchase levels

1.1 Index Numbers

Chapter 6

Data Analysis

- Calculating a Laspeyres Index
- Collect price info for the k price series (the

basket) to be used, denoted as P1t, P2tPkt - Select a base period t0
- Collect purchase quantity info for base period,

denoted as Q1t0, Q2t0..Qkt0 - Calculate weighted totals for each time period

using the formula - Calculate the index using the formula

1.1 Index Numbers

Chapter 6

Data Analysis

- Calculating a Paasche Index
- Collect price info for the k price series to be

used, denoted as P1t, P2tPkt - Select a base period t0
- Collect purchase quantity info for every period,

denoted as Q1t, Q2t..Qkt - Calculate the index for time t using the formula

1.2 Exponential Smoothing

Chapter 6

Data Analysis

- Exponential smoothing is a type of weighted

average that applies a weight w to past and

current values of the time series. (Yi actual

value) - Exponential smoothing constant (w) lies between 0

and 1, and smoothed series Et is calculated as - How much influence
- does the past have when w 0 and

when w 1?

1.2 Exponential Smoothing

Chapter 6

Data Analysis

- Selection of smoothing constant w is made by

researcher. - Small values of w give less weight to current

value, yield a smoother series - Large values of w give more weight to current

value, yield a more variable series

2 Two-way Analysis of Variance

Chapter 6

Data Analysis

- Two-way ANOVA is a type of study design with one

numerical outcome variable and two categorical

explanatory variables. - Example In a completely randomised design we

may wish to compare outcome by age, gender or

disease severity. Subjects are grouped by one

such factor and then randomly assigned one

treatment. - Technical term for such a group is block and the

study design is also called randomised block

design

2 Two-way Analysis of Variance

Chapter 6

Data Analysis

- 2.1 Randomised Block Design
- 2.2 Analysis in Two-way ANOVA 1
- 2.3 Analysis of Two-way ANOVA by the regression

method

2.1 Randomised Block Design

Chapter 6

Data Analysis

- Blocks are formed on the basis of expected

homogeneity of response in each block (or group). - The purpose is to reduce variation in response

within each block (or group) due to biological

differences between individual subjects on

account of age, sex or severity of disease.

2.1 Randomised Block Design

Chapter 6

Data Analysis

- Randomised block design is a more robust design

than the simple randomised design. - The investigator can take into account

simultaneously the effects of two factors on an

outcome of interest. - Additionally, the investigator can test for

interaction, if any, between the two factors.

Steps in Planning a Randomised Block Design

Chapter 6

Data Analysis

2.1 Randomised Block Design

- Subjects are randomly selected to constitute a

random sample. - Subjects likely to have similar response

(homogeneity) are put together to form a block. - To each member in a block intervention is

assigned such that each subject receives one

treatment. - Comparisons of treatment outcomes are made within

each block

2.2 Analysis in Two-way ANOVA - 1

Chapter 6

Data Analysis

- The variance (total sum of squares) is first

partitioned into WITHIN and BETWEEN sum of

squares. Sum of Squares BETWEEN is next

partitioned by intervention, blocking and

interaction

SS TOTAL

SS BETWEEN

SS WITHIN

SS INTERVENTION

SS BLOCKING

SS INTERACTION

Chapter 6

Data Analysis

2.2 Analysis in Two-way ANOVA - 1

method. And an interaction between gender and

teaching method is being sought. Analysis of

Two-way ANOVA is demonstrated in the slides that

follow. The study is about a n experiment

involving a teaching method in which professional

actors were brought in to play the role of

patients in a medical school. The test scores of

male and female students who were taught either

by the conventional method of lectures, seminars

and tutorials and the role-play method were

recorded. The hypotheses being tested

are Role-play method is superior to conventional

way of teaching. Female students in general have

better test scores than male students. Role-play

method makes a better impact on students of a

particular gender. Thus, there are two factors

gender and teaching method. And an interaction

between teaching method and gender is being

sought.

Chapter 6

Data Analysis

2.2 Analysis in Two-way ANOVA - 2

- Each Sum of Squares (SS) is divided by its degree

of freedom (df) to get the Mean Sum of Squares

(MS). - The F statistic is computed for each of the three

ratios as - MS INTERVENTION MS WITHIN
- MS BLOCK MS WITHIN
- MS INTERVENTION MS WITHIN

2.2 Analysis of Two-way ANOVA - 3

Chapter 6

Data Analysis

- Analysis of Variance for score
- Source DF SS MS F

P - sex 1 2839 2839 22.75

0.000 - Tchmthd 1 1782 1782 14.28

0.001 - Error 29 3619 125
- Total 31 8240

2.2 Analysis of Two-way ANOVA - 4

Chapter 6

Data Analysis

- Individual 95 CI
- Sex Mean -------------------------

------------- - 0 58.5

(------------) - 1 39.6 (-------------)
- -------------------------

------------- - 40.0 48.0

56.0 64.0 - Individual 95 CI
- Tchmthd Mean -------------------------

------------- - 0 56.5

(--------------) - 1 41.6 (---------------)
- -------------------------

------------- - 42.0 49.0

56.0 63.0

2.2 Analysis of Tw0-way ANOVA - 5

Chapter 6

Data Analysis

Analysis of Variance for SCORE Source

DF SS MS F

P SEX 1 2839

2839 22.64 0.000 TCHMTHD 1

1782 1782 14.21 0.001 INTERACTN

1 108 108 0.86

0.361 Error 28 3511

125 Total 31 8240

Interaction is not significant P 0.361

2.2 Analysis of Two-way ANOVA - 6

Chapter 6

Data Analysis

Individual 95 CI SEX Mean

-------------------------------------- 0

58.5

(------------) 1 39.6

(-------------)

--------------------------------------

40.0 48.0 56.0

64.0 Individual 95

CI TCHMTHD Mean ----------------------

---------------- 0 56.5

(--------------) 1

41.6 (---------------)

--------------------------------------

42.0 49.0 56.0

63.0

2.3 Analysis of Two-way ANOVA by the regression

method (reference coding)

Chapter 6

Data Analysis

The regression equation is SCORE 65.9 - 18.8

SEX - 14.9 TCHMTHD Predictor Coef

SE Coef T P Constant

65.913 3.420 19.27 0.000 SEX

-18.838 3.950 -4.77

0.000 TCHMTHD -14.925 3.950

-3.78 0.001 S 11.17 R-Sq 56.1

R-Sq(adj) 53.1 Analysis of Variance Source

DF SS MS F

P Regression 2 4620.9

2310.4 18.51 0.000 Residual Error 29

3619.0 124.8 Total 31

8239.8

2.3 Analysis of Two-way ANOVA by the regression

method (effect coding)

Chapter 6

Data Analysis

The regression equation is SCORE 49.0 - 9.42

EFCT-Sex - 7.46 EFCT-Tchmthd - 1.84

Interaction Predictor Coef SE

Coef T P Constant 49.031

1.980 24.77 0.000 EFCT-Sex

-9.419 1.980 -4.76 0.000 EFCT-Tch

-7.463 1.980 -3.77

0.001 Interact -1.838 1.980

-0.93 0.361 S 11.20 R-Sq 57.4

R-Sq(adj) 52.8

Reference Coding and Effect Coding - 1

Chapter 6

Data Analysis

- In both methods, for k explanatory variables k-1

dummy variables are created. - In reference coding the value 1 is assigned to

the group of interest and 0 to all others (e.g.

Female 1 Male 0). - In effect coding the value -1 is assigned to

control group 1 to the group of interest (e.g.

new treatment), and 0 to all others (e.g. Female

1 Male (control group) -1 Role Play 1

conventional teaching (control) -1).

Reference Coding and Effect Coding - 2

Chapter 6

Data Analysis

- In reference coding the ß coefficients of the

regression equation provide estimates of the

differences in means from the control (reference)

group for various treatment groups. - In effect coding the ß coefficients provide the

differences from the overall mean response for

each treatment group.

Chapter 6

Data Analysis

- 3 Marketing Forecasting

3.1 The concept of market forecast 3.2 The

theoretical bases of forecast 3.3 The

classification of forecast methods 3.4

Qualitative Forecast Methods 3.5 Quantitative

Forecast Methods

3.1 The concept of market forecast

Chapter 6

Data Analysis

- Based on market surveys and by applying

scientific methods, to estimate the development

situation of objects-forecasted in a certain

period in future in order to help managers to

improve decisions-making qualify. The process is

generally called as market forecast. - In this chapter, objects-forecasted mainly are

need quantities of products, sometime may also be

product prices, competitive situations,

environmental factors, and so on.

3.2 The theoretical bases of forecast

Chapter 6

Data Analysis

- (1)The continuity principle
- ?It is also called as inertia principle. Because

of existing inertia, any system doesn't change

its basic characteristics in the short run. - Attention all time series analysis methods

are based on this principle.

Chapter 6

Data Analysis

3.2 The theoretical bases of forecast

- (2)The analogy principle
- ?time analogy to make an inference in future

from the past and the present. When two things

and more things have characteristic similarity

(structure, mode, property, and develop

tendency), we can forecast the developing things

and the ready-to-develop things by studying the

developed or advanced things. Attention analogy

is suitable to the homogeneous things, also to

inhomogeneous things.

Chapter 6

Data Analysis

3.2 The theoretical bases of forecast

- (2)The analogy principle
- ?(continual to front page) sampling analogy to

make an inference about the whole from the part.

When the whole and the part have characteristic

similarity, we can forecast the whole by studying

the part. - Attention the similarity is the key point either

between the things with difference in advance

time, or between the whole and the part.

Chapter 6

Data Analysis

3.2 The theoretical bases of forecast

- (3)The relevancy principle
- ?the theory considers that there is relativity

among things, especially between two relevance

things or causal things. All statistical

regression analysis methods are based on this

principle.

3.3 The classification of forecast methods

Chapter 6

Data Analysis

- Although there are many theoretical forecast

methods, in general forecast can be classified as

two types - qualitative forecast
- quantitative forecast.

3.3.1 Qualitative forecast

Chapter 6

Data Analysis

- Qualitative forecast emphasizes the development

tendencies (maybe essential characteristics), and

is suitable to cases which there are a fewer and

lack of data, such as science and technology

forecast, development forecast of infant

industries, long-term forecast, and forecasting

things with uncertainty, etc.

Chapter 6

Data Analysis

3.3.2 Quantitative forecast

- Quantitative forecast emphasizes the quantitative

relationships of developing things. Essentially

it is a kind of methods based on quantitative

trend extrapolation, and is suitable to cases

which there are many data.

Chapter 6

Data Analysis

3.3.3 The comparison of two methods

- Qualitative forecast might contribute to the

analysis of the basic trends, development

inflection point, and the essence of things.

Quantitative forecast can draw us numeral

development concepts, and bring us conveniences

of applying forecast results. None of two methods

should be our preference, otherwise we probably

abuse forecast methods.

3.4 Qualitative Forecast Methods

Chapter 6

Data Analysis

- Delphi method
- Social investigation or consumer survey
- Colligating sellers opinions
- having an informal discussion of a team
- Integration of experts forecasts
- The method of subjective probabilities
- above methods all belong to non-models.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Exponential Smoothing
- ?mathematical model
- ?signs and meanings to explain every sign and

its meaning - ?avalue ais greater, means that the more late

sample observations, the more its influence on

forecast results. Vice versa. Recommendation a

2/(n1)

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Exponential Smoothing
- ?mathematical model----horizontal trend
- ? mathematical model----lineal trend

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Exponential Smoothing
- ?mathematical model---- quadratic curve trend

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Exponential Smoothing
- ?how to choose mathematical models according to

the trend of sample observations on coordinate

diagram.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Exponential Smoothing
- ?how to determine initial values of smoothing

parameters in general, the first observation

value instead of them. - ?superiorities of exponential smoothing the

storage data only is a fewer and it is suitable

to forecast in short run. - ?application cases reference to another teaching

materials.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- The growth curve
- ?mathematical model
- Logistic curve
- Gompertz curve

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- The growth curve
- ?mathematical processing of initial observations
- For Logistic curve
- 2. For Gompertz curve

The processed data of observations can be used

for calculation of parameters k, a and b. The

calculation formulas are as following

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Calculation of k, a, and b

Attention the processed data of observations

must be blacked into 3 groups, thus we can obtain

3 sum values

When the number of initial data is not integer

multiple of 3, we must add or cut down data of

initials.

Chapter 6

Data Analysis

3.5 Quantitative Forecast Methods

- Linear regression
- ?An independent variable and a dependent variable

are chosen on the model, and the varied relation

of y and x is linear. This model is widely

applied in quantitative forecasts. - ?the standard model
- yabx
- to non-standard equation, it is must

transferred as standard model.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression
- ?determination of the coefficient a and b
- by means of method of minimum squares, let

the variance minimization, and the calculation

of is as following - and let derivatives of Q to a and b are equal

to 0, then

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression

We can get a and b

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression
- ?then the forecast model is

It is necessary to check if the model the built

model is of high quality, the checking methods

are 1. standards error analysis

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression
- in general, the following is required

2. correlation coefficient and test of

significance. The calculation of correlation

coefficient is

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression
- ?discussion of correlation coefficient R
- ?when R0, means y doesn't have the correlation

with x, the case is called 0- correlation, so the

built model cant be applied to forecast. - ?when R1, means y has the direct correlation

with x. - ?in general, R is required to meet Rgt0.7. when

Rlt0.3, means the built model can not be applied.

When 0.3ltRlt0.7, means the model is not good and

worthless.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression
- ? The quality of regression model is also tested

by significance. - if , the built model is good and

worth to application. on the contrary, if

, the built model is worthless. - is the critical value of

correlation coefficient R. It is known by looking

up the given table. Theais given level of

significance such as 0.05. The (n-m) is the

degree of freedom such as n-2, m is the number of

variables.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression
- ?the application of model if the future value of

x is known as x?, the interval value of forecast

variable is

Here, s?is determined by the formula

Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression
- and is T-distribution with

significance level aand freedom degree n-m-1,

here n is the number of observations, m is the

number of variables. - ?In addition, many non-linear equation can be

transferred as linear regression. For example

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Linear regression

Then we can get the equation , the

same work is suitable to exponential function,

logarithm function, reciprocal function, etc.

Those functions are called as allowed linear

regression with single variable.

Application case to see another teaching

materials.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- analogy forecasting method a case of

application - ?We can forecast an object variable by

researching the relationship between the variable

and an economic indicator (for example, per

capita national income, NI, or gross national

product, GNP) - ?The relationship between vehicle population and

NI is given in page 78 of textbook.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Elastic coefficient method
- ?For example, we can get the average growth rate

of vehicle sales quantity by observing selling in

the past years, but the rate is only an image. If

we analyzes growth rate of sales together with

growth rate of an economic indicator, we can

improve forecast quality. Detail case is given in

textbook.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- Combination forecasting method
- ?Concept of combination forecasting it is called

as combination forecasting to get a final

forecast conclusion based on colligating multi

intermediate forecast results gained by adopting

multi-models, or on same model adopting multi

independent variables. - ?The core idea combination is benefit to clear

up the chanciness of single mode or independent

variable.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- talking about forecast experience
- ?policy variables it is very difficult to

forecast changes of policy, but we can strengthen

monitoring of environmental factors, especially

paying attention to the running condition of the

national economy. Establishing the monitoring and

early warning system of the national economy is

very necessary.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- talking about forecast experience
- ?predicting accuracy and goodness of fit in

model. - ?simple model and complexity model
- ?single predicting result and many results
- ?reliability of forecast conclusions three pints

are very important----reality initial data

(authoritativeness), accuracy of mathematical

models, and correctness of forecast procedures.

3.5 Quantitative Forecast Methods

Chapter 6

Data Analysis

- talking about forecast experience
- ?data processing, actual cases and researchers

imagination. - to improve forecast, establishing information

system is very important.